Finite Group Databasebeta

← #14575342

Subgroups — #14575342

Order 2432.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597362C211yesmaximal, characteristic, complemented
2#11927205C211yesmaximal, characteristic, complemented
3#11927188C211yesmaximal, characteristic, complemented
4#11926925C211yesmaximal, characteristic, complemented
5#11926773C211yesmaximal, characteristic, complemented
6#11926770C211yesmaximal, characteristic, complemented
7#11926764C211yesmaximal, characteristic, complemented
8#11926761C211yesmaximal, characteristic, complemented
9#11926703C211yesmaximal, characteristic, complemented
10#11926700C211yesmaximal, characteristic, complemented
11#11926688C211yesmaximal, characteristic, complemented
12#11926678C211yesmaximal, characteristic, complemented
13SD16×Dic19C211yesmaximal, characteristic, complemented
14C8×C22⋊D19C211yesmaximal, characteristic, complemented
15C22×SD16×C19C211yesmaximal, characteristic, complemented
16C22×Q8×C19C2211yescharacteristic
17C22×D4×C19C2211yescharacteristic
18C2×#64545C2211yescharacteristic, complemented
19C2×#64543C2211yescharacteristic
20C2×SD16×C19—24no—
21C2×SD16×C19C2211yescharacteristic
22C2×SD16×C19C2211yescharacteristic
23C2×SD16×C19C2211yescharacteristic
24C2×SD16×C19C2211yescharacteristic
25C22×C8×C19C2211yescharacteristic
26#10597399—21no—
27C2×C22⋊Dic19—21no—
28#10597393—21no—
29#10597393C2211yescharacteristic, complemented
30#10597392—21no—
31#10597392C2211yescharacteristic, complemented
32Q8×Dic19C2211yescharacteristic, complemented
33C2×#64528C2211yescharacteristic, complemented
34C2×#64528C2211yescharacteristic, complemented
35#10597385—21no—
36#10597384C2211yescharacteristic
37#10597382C2211yescharacteristic
38#10597381—21no—
39D4×Dic19C2211yescharacteristic
40C2×#64525C2211yescharacteristic
41C2×#64525C2211yescharacteristic
42#10597376—21no—
43#10597376C2211yescharacteristic
44C4×C22⋊D19—21no—
45C4×C22⋊D19C2211yescharacteristic
46#10597370C2211yescharacteristic
47#10597362—24no—
48C2×#64516C2211yescharacteristic, complemented
49C2×C8×D19C2211yescharacteristic, complemented
50#10597292C2211yescharacteristic, complemented
51#10597292C2211yescharacteristic, complemented
52#10597289C2211yescharacteristic
53#10597289C2211yescharacteristic
54C22⋊(C19⋊C8)C2211yescharacteristic
55#10597278C2211yescharacteristic, complemented
56(C2×D19)⋊C8C2211yescharacteristic, complemented
57#10597274C2211yescharacteristic, complemented
58#10597273C2211yescharacteristic, complemented
59Dic19⋊C8C2211yescharacteristic, complemented
60C8×Dic19C2211yescharacteristic, complemented
61C24×C19—21no—
62C2×Q8×C19—21no—
63C2×Q8×C19—22no—
64C2×Q8×C19—41no—
65C2×Q8×C19C2311yescharacteristic
66C2×Q8×C19C2311yescharacteristic
67C2×D4×C19—22no—
68C2×D4×C19—21no—
69C2×D4×C19—41no—
70C2×D4×C19C2311yescharacteristic
71C2×D4×C19C2311yescharacteristic
72C22×C4×C19—21no—
73C22×C4×C19C2311yescharacteristic
74C2×C22⋊D19—21no—
75C2×C22⋊D19—21no—
76C2×C22⋊D19—21no—
77C2×C22⋊D19D411yescharacteristic
78C22×Dic19—21no—
79C22×Dic19—21no—
80#64545—22no—
81#64545—41no—
82#64543—22no—
83#64543—41no—
84C2×D76—21no—
85C2×D76C2311yescharacteristic
86C2×C4×D19—21no—
87C2×C4×D19C2311yescharacteristic
88C2×Dic38C2311yescharacteristic
89SD16×C19—22no—
90SD16×C19—22no—
91SD16×C19—22no—
92SD16×C19D414yescomplemented
93C2×C8×C19—22no—
94C2×C8×C19C2311yescharacteristic
95C2×C8×C19C2311yescharacteristic
96C22⋊Dic19—21no—
97C22⋊Dic19—21no—
98C22⋊Dic19—21no—
99C22⋊Dic19—21no—
100C22⋊Dic19—21no—
101C22⋊Dic19D411yescharacteristic
102#64528—22no—
103#64528—41no—
104#64525—22no—
105#64525—41no—
106(C2×D19)⋊C4—21no—
107(C2×D19)⋊C4—21no—
108(C2×D19)⋊C4—21no—
109(C2×D19)⋊C4—21no—
110(C2×D19)⋊C4D411yescharacteristic
111C4⋊Dic19—21no—
112C4⋊Dic19C2311yescharacteristic
113C4⋊Dic19C2311yescharacteristic
114Dic19⋊C4—21no—
115Dic19⋊C4—21no—
116Dic19⋊C4D411yescharacteristic
117C4×Dic19—21no—
118C4×Dic19C2311yescharacteristic
119C2×C19⋊C8C2311yescharacteristic
120C2×C19⋊C8C2311yescharacteristic
121#64516—22no—
122C8×D19—22no—
123C23×C19—21no—
124C23×C19—21no—
125C23×C19—42no—
126C23×C19—42no—
127C23×C19—81no—
128C23×C19C2×D411yescharacteristic
129C22×D19—21no—
130C22×D19C2×D411yescharacteristic
131Q8×C19—21no—
132Q8×C19—21no—
133Q8×C19—21no—
134Q8×C19—42no—
135Q8×C19C2×D412yes—
136D4×C19—21no—
137D4×C19—21no—
138D4×C19—21no—
139D4×C19—42no—
140D4×C19C2×D412yes—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—42no—
146C2×C4×C19C2×D411yescharacteristic
147C2×C4×C19C2411yescharacteristic
148C22⋊D19—22no—
149C22⋊D19—42no—
150C22⋊D19—42no—
151C22⋊D19—81no—
152C2×Dic19—21no—
153C2×Dic19—21no—
154C2×Dic19—21no—
155C2×Dic19—42no—
156C2×Dic19—81no—
157C2×Dic19C2×D411yescharacteristic
158C2×Dic19C2×D411yescharacteristic
159C2×Dic19C2×D411yescharacteristic
160D76—21no—
161D76—21no—
162D76—42no—
163C4×D19—21no—
164C4×D19—21no—
165C4×D19—42no—
166Dic38—21no—
167Dic38—21no—
168C8×C19—21no—
169C8×C19C2×D412yes—
170C19⋊C8—21no—
171C19⋊C8—21no—
172#3282—191nomaximal, Sylow
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—22no—
176C22×C19—41no—
177C22×C19—41no—
178C22×C19—41no—
179C22×C19—41no—
180C22×C19—41no—
181C22×C19—84no—
182C22×C19#13512yescomplemented
183C22×C19C22×D411yescharacteristic
184C2×D19—21no—
185C2×D19—21no—
186C2×D19—21no—
187C2×D19—41no—
188C2×D19—41no—
189C2×D19—41no—
190C4×C19—22no—
191C4×C19—21no—
192C4×C19—41no—
193C4×C19C22×D411yescharacteristic
194C4×C19H(5,𝔽2)11yescharacteristic
195Dic19—21no—
196Dic19—21no—
197Dic19—21no—
198Dic19—41no—
199Dic19—41no—
200Dic19—41no—
201C2×#135—191no—
202C22×SD16D1911yescharacteristic, complemented
203#548—191no—
204#546—191no—
205#495—191no—
206#465—191no—
207#465—191no—
208#464—191no—
209#463—191no—
210#452—191no—
211#451—191no—
212#449—191no—
213#447—191no—
214C4×SD16—191no—
215C8×D4—191no—
216C2×C19—22no—
217C2×C19—42no—
218C2×C19—81no—
219C2×C19D4211yescharacteristic
220C2×C19C2×#13511yescharacteristic
221C2×C19#57711yescharacteristic
222D19—41no—
223D19—81no—
224C2×#41—191no—
225C2×#41—191no—
226C22×Q8C2×D1911yescharacteristic
227C22×D4C2×D1911yescharacteristic
228#135—384no—
229C2×Q16—191no—
230C2×Q16—191no—
231C2×SD16—24no—
232C2×SD16—191no—
233C2×SD16C2×D1911yescharacteristic
234C2×SD16C2×D1911yescharacteristic
235C2×SD16C2×D1911yescharacteristic
236C2×SD16C2×D1911yescharacteristic
237C2×D8—191no—
238C2×D8—191no—
239C22×C8—191no—
240C22×C8C2×D1911yescharacteristic
241#124—191no—
242#124—191no—
243#124—381no—
244#123—381no—
245C22⋊Q8—191no—
246C22⋊Q8—191no—
247C22⋊Q8—381no—
248#121—191no—
249#121—191no—
250#121—381no—
251#121—381no—
252#120—381no—
253C4×Q8—191no—
254C4×D4—191no—
255C4×D4—191no—
256C4×D4—381no—
257C2×C22⋊C4—381no—
258#106—191no—
259C4⋊C8—191no—
260#103—191no—
261#103—191no—
262#103—191no—
263#102—191no—
264#102—191no—
265#102—191no—
266C22⋊C8—191no—
267C22⋊C8—191no—
268C4×C8—191no—
269C19#328211yescharacteristic, complemented, Sylow
270C24—21no—
271#41—382no—
272#41—382no—
273#41—761no—
274#41—761no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—191no—
279C2×Q8C22×D1911yescharacteristic
280C2×Q8C22×D1911yescharacteristic
281C2×D4—22no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4—191no—
285C2×D4—191no—
286C2×D4—381no—
287C2×D4—381no—
288C2×D4—381no—
289C2×D4—381no—
290C2×D4C22×D1911yescharacteristic
291C2×D4C22×D1911yescharacteristic
292C22×C4—21no—
293C22×C4—191no—
294C22×C4—381no—
295C22×C4—381no—
296C22×C4—381no—
297C22×C4C22×D1911yescharacteristic
298Q16—382no—
299Q16—761no—
300SD16—22no—
301SD16—22no—
302SD16—22no—
303SD16—382no—
304SD16C22⋊D1914yescomplemented
305D8—382no—
306D8—761no—
307C2×C8—22no—
308C2×C8—191no—
309C2×C8—191no—
310C2×C8—382no—
311C2×C8C22×D1911yescharacteristic
312C2×C8C22×D1911yescharacteristic
313C4⋊C4—191no—
314C4⋊C4—191no—
315C4⋊C4—191no—
316C4⋊C4—381no—
317C4⋊C4—381no—
318C4⋊C4—381no—
319C22⋊C4—191no—
320C22⋊C4—191no—
321C22⋊C4—381no—
322C22⋊C4—381no—
323C22⋊C4—381no—
324C22⋊C4—381no—
325C22⋊C4—381no—
326C22⋊C4—381no—
327C22⋊C4—381no—
328C22⋊C4—381no—
329C22⋊C4—381no—
330C42—191no—
331C42—381no—
332C23—21no—
333C23—21no—
334C23—42no—
335C23—42no—
336C23—81no—
337C23—191no—
338C23—381no—
339C23D4×D1911yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—42no—
344Q8—381no—
345Q8—381no—
346Q8C2×C22⋊D1912yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—42no—
351D4—382no—
352D4—381no—
353D4—381no—
354D4—762no—
355D4—762no—
356D4—762no—
357D4—1521no—
358D4C2×C22⋊D1912yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—191no—
365C2×C4—191no—
366C2×C4—191no—
367C2×C4—381no—
368C2×C4—381no—
369C2×C4—381no—
370C2×C4—381no—
371C2×C4—381no—
372C2×C4—762no—
373C2×C4—762no—
374C2×C4—1521no—
375C2×C4D4×D1911yescharacteristic
376C2×C4C23×D1911yescharacteristic
377C8—21no—
378C8—381no—
379C8—381no—
380C8C2×C22⋊D1912yes—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—84no—
390C22—381no—
391C22—381no—
392C22—381no—
393C22—761no—
394C22—761no—
395C22—761no—
396C22#1059736212yescomplemented
397C22C2×D4×D1911yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—381no—
402C4—381no—
403C4—381no—
404C4—761no—
405C4—761no—
406C4—761no—
407C4#1059743011yescharacteristic
408C4C22×C22⋊D1911yescharacteristic
409C2—22no—
410C2—42no—
411C2—81no—
412C2—761no—
413C2—1521no—
414C2D4×C22⋊D1911yescharacteristic
415C2C2×#1059736211yescharacteristic
416C2#1192735011yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC22×SD16×C19C2
socleC22×C19C22×D4
hypercenterC22×SD16D19
hypocenterC19#3282
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10597362C2semidirect
2. #11927205C2semidirect
3. #11927188C2semidirect
4. #11926925C2semidirect
5. #11926773C2semidirect
6. #11926770C2semidirect
7. #11926764C2semidirect
8. #11926761C2semidirect
9. #11926703C2semidirect
10. #11926700C2semidirect
11. #11926688C2semidirect
12. #11926678C2semidirect
13. SD16×Dic19C2semidirect
14. C8×C22⋊D19C2semidirect
15. C22×SD16×C19C2semidirect
18. C2×#64545C22semidirect
29. #10597393C22semidirect
31. #10597392C22semidirect
32. Q8×Dic19C22semidirect
33. C2×#64528C22semidirect
34. C2×#64528C22semidirect
48. C2×#64516C22semidirect
49. C2×C8×D19C22semidirect
50. #10597292C22semidirect
51. #10597292C22semidirect
55. #10597278C22semidirect
56. (C2×D19)⋊C8C22semidirect
57. #10597274C22semidirect
58. #10597273C22semidirect
59. Dic19⋊C8C22semidirect
60. C8×Dic19C22semidirect
92. SD16×C19D4semidirect
182. C22×C19#135semidirect
202. C22×SD16D19semidirect
269. C19#3282semidirect
304. SD16C22⋊D19semidirect
396. C22#10597362semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#105973622
#119272052
#119271882
#119269252
#119267732
#119267702
#119267642
#119267612
#119267032
#119267002
#119266882
#119266782
SD16×Dic192
C8×C22⋊D192
C22×SD16×C192
#328219